Parameters Δi Research Articles

On stretching of plasma parameters and related open issues for the study of dust-ion-acoustic and dust-acoustic shock waves in dusty plasmas

To study the properties of the shock structures associated with dust-ion-acoustic (DIA) and dust-acoustic (DA) waves, the stretching of the plasma parameters [viz., kinematic or longitudinal viscosity coefficient ηi (ηd) for DIA (DA) waves and the plasma parameter δi (δd) associated with the dust charge fluctuation for DIA (DA) waves] has been used by many authors. It is argued that the stretching of such plasma parameters is not usually valid. The valid stretching coordinates for deriving the Burgers equation, which leads to the formation of DIA and DA shock waves, are provided. A few open issues related to the sources of dissipation [viz., different viscous forces giving rise to ηi and ηd and dust charge fluctuation giving rise to δi and δd] are also pinpointed. To remove the stretching of plasma parameters, which is not usually valid, from our future research work, and to address some related open issues will be able not only to enhance the quality of our future research work but also to help us in working on some challenging research problems in dusty plasma physics.

In-gap bound states induced by interstitial Fe impurities in iron-based superconductors

Based on a two-orbit four-band tight binding model, we investigate the low-lying electronic states around the interstitial excess Fe ions in the iron-based superconductors by using T-matrix approach. It is shown that the local density of states at the interstitial Fe impurity (IFI) possesses a strong resonance inside the gap, which seems to be insensitive to the doping and the pairing symmetry in the Fe–Fe plane, while a single or two resonances appear at the nearest neighboring (NN) Fe sites. The location and height of the resonance peaks only depend on the hopping t and the pairing parameter ΔI between the IFI and the NN Fe sites. These in-gap resonances are originated in the Andreev’s bound states due to the quasiparticle tunneling through the IFI, leading to the change of the magnitude of the superconducting order parameter. When both t and ΔI are small, this robust zero-energy bound state near the IFI is consistent with recent scanning tunneling microscopy observations.

The n-level, n − 1-mode Jaynes–Cummings model: spectrum and eigenvectors

We explicitly find eigenvectors and eigenvalues of the general n-level, n − 1-mode Jaynes–Cummings model in Λ-configuration possessing arbitrary detuning parameters Δi, and arbitrary interaction strengths gi, . In the case of equal interaction strengths gi = gj, , we compare the obtained answers with those obtained by the algebraic Bethe ansatz method (Skrypnyk 2008 J. Phys. A: Math. Theor. 41 475202; 2009 J. Math. Phys. 50 103523).

Beats of quantum oscillations of the hall coefficient and resistivity in semiconductor alloys n-Bi0.93Sb0.07 at a small deviation of the magnetic field direction from the trigonal axis

Quantum oscillations of the resistivity ρ22 and Hall coefficient R 12.3 in the semiconductor alloy n-Bi0.93Sb0.07 have been studied at H ‖ C 3 and j ‖ C 1 in magnetic fields to 14 T and at temperatures of 1.5, 4.5, 10, and 20 K. At temperatures of 1.5 and 4.5 K, beats of quantum oscillations of ρ22 and R 12.3 due to a small deviation of the magnetic field H from the crystallographic C 3 axis have been observed. To determine the oscillation period Δ i , cyclotron mass m ci , cyclotron frequency ω ci , and extreme section S extri, experimentally measured quantum oscillation beats have been compared with the model beats of oscillations of three harmonic functions, two of which have close frequencies. The deviation of the parameters Δ i , m ci , and S extri from the same parameters when the magnetic field H exactly coincides with the trigonal C 3 axis has made it possible to estimate the magnetic field H deflection angle from the trigonal C 3 axis, which is ∼1°.

Steady-State Electrochemical Determination of Lipidic Nanotube Diameter Utilizing an Artificial Cell Model

By exploiting the capabilities of steady-state electrochemical measurements, we have measured the inner diameter of a lipid nanotube using Fick's first law of diffusion in conjunction with an imposed linear concentration gradient of electroactive molecules over the length of the nanotube. Fick's law has been used in this way to provide a direct relationship between the nanotube diameter and the measurable experimental parameters Deltai (change in current) and nanotube length. Catechol was used to determine the Deltai attributed to its flux out of the nanotube. Comparing the nanotube diameter as a function of nanotube length revealed that membrane elastic energy was playing an important role in determining the size of the nanotube and was different when the tube was connected to either end of two vesicles or to a vesicle on one end and a pipet tip on the other. We assume that repulsive interaction between neck regions can be used to explain the trends observed. This theoretical approach based on elastic energy considerations provides a qualitative description consistent with experimental data.

A nonhomogeneous risk process with fixed number of payments

Let x ≥ 0 be the initial capital, T1, T2, . . . be the times of payments, 0 ≤ T1 ≤ T2 ≤ . . . , Zi be the payment value at time Ti, and ∆i = Ti − Ti−1, i > 1, ∆1 = T1. We assume that {Zi} and {∆i} are independent sequences of independent random variables. The risk process linearly increases at each of the intervals ∆i with slope ci ≥ 0. The variables Zi are exponentially distributed with parameters μi, while ∆i are exponentially distributed with parameters δi. The difference of such a risk process from the classical one consists of the fact that in the classical process the parameters μi, δi, and ci, i ≥ 1, do not depend on i. Let ri be the vector (δi, ci, μi), βi = δi ci , λi = βi μi + βi . Let the number of payments be finite and equal to n, and let Ψn(x, r1, r2, . . . , rn) and Rn(x, r1, r2, . . . , rn) be the probabilities of ruin and nonruin, respectively. As in the classical case, ruin occurs in n payments if there exists k, k ≤ n, such that xk < 0, where xk is the capital after the kth payment. It is easy to see that

Many-particle effects in the bond length alternation of alternant hydrocarbons

The local approach (LA) method has been employed to investigate the correlated ground state wavefunction in alternant monocyclic and linear hydrocarbon π systems as a function of the bond length alternation δ. The LA has been supplemented by a simple model-Hamiltonian developed in the ZDO (zero differential overlap) approximation. The integrals have been calculated ab initio in a Slater-type basis. To quantify many-particle effects in the studied systems we have determined the interatomic π correlation energy E corr and a π electron localization parameter Δi as a function of δ. Δi measures the reduction of the charge fluctuations due to electronic correlations and is thus a convenient measure for the atomic electron density localization. It is demonstrated that monocyclic 4n + 2 (n = 1,2,3, …) Huckel rings allow for a coincidence of increasing |E corr| numbers and increasing atomic electron density delocalization with enlarged δ values. The δ variation of Δi reflects in a transparent form that hydrocarbon...

Solvent‐induced isotope effects in NMR spectroscopy. A study of hydrogen bonding between the carbonyl group in chalcone and trifluoracetic acid (TFA‐d or TFA) in chloroform solution

AbstractSplittings, δi, were observed for each carbon atom, Ci, of chalcone in spectra obtained from coaxial 5 and 10 mm NMR sample tubes containing solutions equimolar in the concentration of the ketone and of TFA or TFA‐d as hydrogen‐bond donors, respectively. It was found that a linear expression, δi = (K–1)xHΔi+xDδi(D, H) relates these splittings, δi, induced by the isotopic substitution in a hydrogen bond, to the parameter Δi, denoting the change in chemical shift for each carbon site in complexed and free ketone, and δi(D, H), the solvent‐induced isotope effect in a complex. The origin of the phenomenon is briefly discussed. It is also shown that the secondary deuterium isotope effect can give the same information about the form of the potential energy well in the hydrogen‐bond as the primary H/D isotopte shifts.